3. A vacation home in Orlando, Florida, rents for $105 per day. The function f(x) = 105x gives the cost of renting the home for x days. What is the domain of this function?
I'd guess non-negative integers (up to some reasonable maximum)
The domain of a function refers to the set of possible input values or x-values for which the function is defined. In this case, the function f(x) = 105x gives the cost of renting the home for x days.
Since x represents the number of days, it must be a positive integer. The minimum value for x would be 1 day because it doesn't make sense for the number of days to be zero or negative when renting a vacation home. There is no maximum limit to the number of days that can be rented.
Therefore, the domain of the function is all positive integers: {1, 2, 3, 4, ... }.
To determine the domain of the function f(x) = 105x, we need to consider the values that x can take that make the function meaningful. In this case, x represents the number of days that the vacation home is rented for.
Since the number of days cannot be negative (as you cannot rent a home for a negative amount of time), and it is unlikely that the vacation home can be rented for an infinite number of days, we can assume that the domain of this function is restricted to non-negative real numbers (x ≥ 0).
Therefore, the domain of the function f(x) = 105x is x ≥ 0.